Select The Best Answer For The Question.9. Find The Quotient Of $5 / 31$ Divided By $15 / 23$. Reduce Your Answer To The Lowest Fraction.A. 93 / 23 ^{93} / 23 93 /23 , Or 4 1 23 4 \frac{1}{23} 4 23 1 B. 23 / 93 ^{23 / 93} 23/93 C. $^{75} /
Introduction
In mathematics, fractions are a fundamental concept that plays a crucial role in various mathematical operations. When dealing with fractions, it's essential to understand how to perform operations such as division, multiplication, and addition. In this article, we will focus on solving the quotient of fractions, specifically the problem of finding the quotient of $5 / 31$ divided by $15 / 23$. We will break down the solution into manageable steps and provide a clear explanation of each step.
Understanding the Problem
The problem requires us to find the quotient of $5 / 31$ divided by $15 / 23$. To solve this problem, we need to understand the concept of dividing fractions. When dividing fractions, we can invert the second fraction (i.e., flip the numerator and denominator) and then multiply the fractions.
Step 1: Invert the Second Fraction
To solve the problem, we need to invert the second fraction, which is $15 / 23$. Inverting this fraction means flipping the numerator and denominator, resulting in $23 / 15$.
Step 2: Multiply the Fractions
Now that we have inverted the second fraction, we can multiply the fractions. To multiply fractions, we multiply the numerators and denominators separately. In this case, we multiply $5$ by $23$ and $31$ by $15$.
Step 3: Simplify the Fraction
After multiplying the fractions, we need to simplify the resulting fraction. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.
In this case, the numerator is $5 \times 23 = 115$ and the denominator is $31 \times 15 = 465$. The GCD of $115$ and $465$ is $5$.
Step 4: Reduce the Fraction to Lowest Terms
Finally, we need to reduce the fraction to its lowest terms. To reduce a fraction, we need to find the GCD of the numerator and denominator and divide both numbers by the GCD.
In this case, the numerator is $23$ and the denominator is $93$. The GCD of $23$ and $93$ is $1$.
Since the GCD is $1$, the fraction $\frac{23}{93}$ is already in its lowest terms.
Conclusion
In conclusion, the quotient of $5 / 31$ divided by $15 / 23$ is $\frac{23}{93}$. This fraction cannot be reduced further, and it is already in its lowest terms.
Answer Options
Based on the solution, we can evaluate the answer options provided:
A. , or : This option is incorrect because the correct answer is $\frac{23}{93}$, not $\frac{93}{23}$.
B. : This option is correct because it matches the solution we obtained.
C. : This option is incorrect because the correct answer is $\frac{23}{93}$, not $\frac{75}{23}$.
Final Answer
The final answer is:
Q: What is the quotient of fractions?
A: The quotient of fractions is the result of dividing one fraction by another. When dividing fractions, we can invert the second fraction (i.e., flip the numerator and denominator) and then multiply the fractions.
Q: How do I invert a fraction?
A: To invert a fraction, we simply flip the numerator and denominator. For example, if we have the fraction $\frac{a}{b}$, the inverted fraction would be $\frac{b}{a}$.
Q: How do I multiply fractions?
A: To multiply fractions, we multiply the numerators and denominators separately. For example, if we have the fractions $\frac{a}{b}$ and $\frac{c}{d}$, the product would be $\frac{a \times c}{b \times d}$.
Q: How do I simplify a fraction?
A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. This will result in a fraction that is in its lowest terms.
Q: What is the greatest common divisor (GCD)?
A: The GCD is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder. For example, if we have the fraction $\frac{12}{18}$, the GCD is $6$ because $6$ is the largest number that divides both $12$ and $18$ without leaving a remainder.
Q: How do I reduce a fraction to its lowest terms?
A: To reduce a fraction to its lowest terms, we need to find the GCD of the numerator and denominator and divide both numbers by the GCD. This will result in a fraction that is in its lowest terms.
Q: What is the difference between dividing fractions and multiplying fractions?
A: Dividing fractions involves inverting the second fraction and then multiplying the fractions. Multiplying fractions involves multiplying the numerators and denominators separately.
Q: Can I simplify a fraction by canceling out common factors?
A: Yes, you can simplify a fraction by canceling out common factors. This is a shortcut method of simplifying fractions that involves canceling out common factors between the numerator and denominator.
Q: What are some common mistakes to avoid when solving the quotient of fractions?
A: Some common mistakes to avoid when solving the quotient of fractions include:
- Inverting the wrong fraction
- Multiplying the fractions incorrectly
- Failing to simplify the fraction
- Canceling out common factors incorrectly
Q: How can I practice solving the quotient of fractions?
A: You can practice solving the quotient of fractions by working through examples and exercises. You can also use online resources and practice tests to help you improve your skills.
Conclusion
Solving the quotient of fractions requires a clear understanding of the concepts of inverting fractions, multiplying fractions, and simplifying fractions. By following the steps outlined in this article, you can confidently solve the quotient of fractions and improve your math skills.